{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _nb_kktpm:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Karush Kuhn Tucker Proximity Measure (KKTPM)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In 2016, Deb and Abouhawwash proposed Karush Kuhn Tucker Proximity Measure (KKTPM) <cite data-cite=\"kktpm1\"></cite>, a metric that can measure how close a point is from being “an optimum”. The smaller the metric, the closer the point. This does not require the Pareto front to be known, but the gradient information needs to be approximated.\n",
    "Their metric applies to both single objective and multi-objective optimization problems. \n",
    "\n",
    "In a single objective problem, the metric shows how close a point is from being a “local optimum”, while in multi-objective problems, the metric shows how close a point is from being a “local Pareto point”. Exact calculations of KKTPM for each point requires solving a whole optimization problem, which is extremely time-consuming. To avoid this problem, the authors of the original work again proposed several approximations to the true KKTPM, namely Direct KKTPM, Projected KKTPM, Adjusted KKTPM, and Approximate KKTPM. Approximate KKTPM is simply the average of the former three and is what we call simply “KKTPM”. Moreover, they were able to show that Approximate KKTPM is reliable and can be used in place of the exact one <cite data-cite=\"kktpm2\"></cite>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"display: block;margin-left: auto;margin-right: auto;width: 50%;\">\n",
    "![nsga2_crowding](../resources/images/kktpm.png)\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now see how to use pymoo to calculate the KKTPM for point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pymoo.factory import get_problem\n",
    "problem = get_problem(\"zdt1\", n_var=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For instance, the code below calculates the KKTPM metric for randomly sampled points for the given an example;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pymoo.performance_indicator.kktpm import KKTPM\n",
    "from pymoo.operators.sampling.random_sampling import FloatRandomSampling\n",
    "\n",
    "X = FloatRandomSampling().do(problem, 100).get(\"X\")\n",
    "kktpm = KKTPM().calc(X, problem)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Moreover, a whole run of a genetic algorithm can be analyzed by storing each generation's history and then calculating the KKTPM metric for each of the points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pymoo.algorithms.nsga2 import NSGA2\n",
    "from pymoo.factory import get_problem\n",
    "from pymoo.optimize import minimize\n",
    "from pymoo.visualization.scatter import Scatter\n",
    "\n",
    "algorithm = NSGA2(pop_size=100, eliminate_duplicates=True)\n",
    "\n",
    "res = minimize(problem,\n",
    "               algorithm,\n",
    "               ('n_gen', 100),\n",
    "               seed=1,\n",
    "               save_history=True,\n",
    "               verbose=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "_min, _median, _max = [], [], []\n",
    "\n",
    "for a in res.history:\n",
    "    X = a.pop.get(\"X\")\n",
    "    kktpm = KKTPM().calc(X, problem)\n",
    "    \n",
    "    _min.append(kktpm.min())\n",
    "    _median.append(np.median(kktpm))\n",
    "    _max.append(kktpm.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 379
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "I = np.arange(len(res.history))\n",
    "plt.plot(I, _min, label=\"Min\")\n",
    "plt.plot(I, _median, label=\"Median\")\n",
    "plt.plot(I, _max, label=\"Max\")\n",
    "plt.yscale(\"log\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
